Omni Calculator logo

Resonant Frequency Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jan 18, 2024


If you would like to calculate the resonant frequency of an LC circuit, look no further - this resonant frequency calculator is the tool for you. Enter the inductance and capacitance and in no time at all you'll find the resonant and angular frequency. We also provide some theory as it may be handy - below you'll find out how to calculate resonant frequency as well as a short definition about what the resonant frequency actually is.

If you're interested in electronic circuits, you would probably like to know how to obtain some fraction of input voltage - our voltage divider calculator is a must for that task.

What is an LC circuit (tank circuit)?

An LC circuit (also called a resonant circuit, tank circuit, or tuned circuit) is an idealized RLC circuit of zero resistance. If you are looking for the "non-ideal" circuit, head to our RLC circuit calculator!

An LC circuit contains only an inductor and a capacitor, in a parallel or series configuration:

Parallel LC Circuit
Parallel LC Circuit
Series LC Circuit
Series LC Circuit

Tank circuits are commonly used as signal generators and bandpass filters - meaning that they're selecting a signal at a particular frequency from a more complex signal. They are widely applied in electronics - you can find LC circuits in amplifiers, oscillators, tuners, radio transmitters and receivers. LC and RC circuits can be used to filter a signal by blocking certain frequencies.

🙋 Omni has other great tools to help you in your electronics studies: try our RC circuit calculator or our collection of tools for simple circuits:

What is a resonant frequency?

The resonant frequency is a natural, undamped frequency of a system. If we apply a resonant frequency, the oscillations become the maximum amplitude, and even relatively small forces can produce large amplitudes. However, if any other frequency is chosen, that signal is dampened.

There are many different types of resonances, e.g.:

  • Mechanical and acoustic;
  • Electrical;
  • Optical;
  • Orbital; and
  • Molecular.

For LC circuits, the resonant frequency is determined by the capacitance C and the impedance L.

How do you calculate the resonant frequency of an LC circuit?

To calculate the resonant frequency of a circuit composed of an inductor and a capacitor, follow these steps:

  1. Write down the capacitance C in farads.
  2. Write down the inductance L in henries.
  3. Input both parameters in the resonant frequency formula: f = 1 / (2π × √(L × C)).

Where:

  • ff — The resonant frequency;
  • LL — The circuit inductance; and
  • CC — The circuit capacitance.

Where does this formula come from? Resonance in the LC circuit appears when the inductive reactance of the inductor becomes equal to the capacitive reactance of the capacitor. So:

xL=2πfLxL = 2\pi\cdot f\cdot L
xC=12πfCxC = \frac{1}{2\pi\cdot f\cdot C}

Then, after transforming the equation, we find:

xL=xC2πfL=12πfC\begin{split} xL&=xC\\ 2\pi\cdot f\cdot L&=\frac{1}{2\pi\cdot f\cdot C} \end{split}

So:

f2=14π2LCf^2 = \frac{1}{4\pi^2\cdot L \cdot C}

And finally:

f=12πLCf = \frac{1}{2\pi\sqrt{L\cdot C}}

Also, the angular frequency may be calculated from the following, well-known formula:

ω=2πf\omega = 2\cdot \pi \cdot f

How to use the resonant frequency calculator

Using our tool is a walk in the park:

  1. Enter the capacitor value. For example, our capacitance is equal to 1 μF1\ \mathrm{μF}.
  2. Type the inductance. Our inductor in our LC circuit equals 0.18 mH0.18\ \mathrm{mH}.
  3. The resonant frequency calculator did the job! We quickly found out what the resonant frequency is: 11.863 kHz. If you want to check the angular frequency as well, just hit the Advanced mode button and the result will appear underneath.

A resonant frequency calculator is a flexible tool, so - as usual - you can type any two variables, and the missing one will be calculated in a flash.

FAQ

What's the resonant frequency if C=220 pF and L=1 mH?

339.32 kHz. In an LC circuit where the capacitance is 220 pF = 2.20×10^(-10) F and the inductance is 1 mH = 0.001 H, the resonant frequency is: f = 1 / (2π × √(2.20×10^(-10) × 0.001)) = 339,319 Hz ≈ 339.32 kHz.

How do radios use the resonant frequency?

When you select a specific radio station, you are tuning the resonant frequency of the LC circuit within the radio to match the frequency of the incoming signal, filtering out any other signals.

Hanna Pamuła, PhD
Capacitance (C)
pF
Inductance (L)
μH
Resonant frequency (f)
MHz
Parallel LC CircuitSeries LC Circuit
Check out 51 similar electronics and circuits calculators 💡
Breaker sizeBridge rectifierCapacitor charge time… 48 more
People also viewed…

Fulcrum

Use this fulcrum calculator to determine a lever's fulcrum location from the load you want to lift.

Podcasts

Do you feel like you could be doing something more productive or educational while on a bus? Or while cleaning the house? Well, why don't you dive into the rich world of podcasts! With this podcast calculator, we'll work out just how many great interviews or fascinating stories you can go through by reclaiming your 'dead time'!

Sunbathing

Do you always remember to put on sunscreen before going outside? Are you sure that you use enough? The Sunbathing Calculator ☀ will tell you when's the time to go back under an umbrella not to suffer from a sunburn!

Wave speed

Calculate the speed of waves using the wave speed calculator.